IC design modeling allowing dimension-dependent rule checking

ABSTRACT

A method, system and program product to model an IC design to include dimensions such as a local width and spacing of IC shapes in a consistent fashion. In particular, the invention uses a core portion of Voronoi diagrams to partition edges of a shape into intervals and assigns at least one dimension to each interval such as a local width and spacing. Dimension assignment can be made as any desirable definition set for width and spacing, e.g., numerical values or continuous dimension-dependent design rules. Design rule checking for dimension-dependent spacing rules given in any arbitrary functional form of width and spacing is possible. Application of the invention can be made anywhere the width and spacing of VLSI shapes play a role, e.g., relative to a single edge, neighboring edges, neighboring shapes, and/or for edges in more than one layer of the IC design.

BACKGROUND OF INVENTION

1. Technical Field

The present invention relates generally to integrated circuit design,and more particularly, to integrated circuit design modeling that allowsfor dimension-dependent rule checking.

2. Related Art

Very large scale integrated (VLSI) circuits are designed usingcomputer-implemented design systems that allow a designer to generateand test a circuit design before the more expensive manufacturing of theintegrated circuit (IC). In order to ensure proper design of an IC, eachdesign system and/or IC format includes a set of design rules that eachcircuit design must meet. That is, each IC design must pass a designrule check (DRC). One fundamental operation of DRC isdimension-dependent rule checking. Dimension-dependent rule checkingensures that dimensions, namely width and spacing, of parts of an ICmeet a specific dimensional parameter, e.g., a size range. Among themost significant dimension-dependent rule checking are thewidth-dependent and spacing-dependent rules that prevent IC parts frombeing too large/small or too close together/too far apart.

Current DRC tools derive width and spacing of VLSI shapes usingone-dimensional visibility or standard “shape-expand” and “shape-shrink”operations. Advancements in IC design have resulted in the variousshapes of IC parts becoming more complex than simple rectangles. As aresult, defining what is a “width” of a shape(s), or what is the“spacing” between shapes has become difficult and inconsistent. Inparticular, the conventional mathematical definition of “width” of anypolygon is the smallest distance between any two parallel lines ofsupport. This definition implies a unique width for any shape based onits convex hull. (Note that typically an IC non-convex polygon can bemuch more “narrow” than its associated convex hull, e.g., an L-shape).However, this definition is not appropriate for DRC among non-convexshapes as it assigns the unique width of the convex hull to the wholeshape.

Where a DRC method uses one-dimensional (1D) visibility, the width orspacing near a vertical edge is often determined by other vertical edgesthat this edge can “see” along the horizontal direction. This approachis adequate in some cases but it often leads to results that areinconsistent as 1D visibility is not appropriate to characterize thewidth of a shape. For example, for any edge having a distance to anotheredge that varies along its length results in the width beinginconsistent or indeterminable. Currently, there is no consistent orsatisfactory definition for the “width” of an arbitrary shape(s) otherthan a rectangle. The above-described problem applies tospacing-dependent design rules also.

With regard to “expand” and “shrink” operations, most modern shapeprocessing tools have functions that expand or shrink a shape by a givenconstant amount. The results of these operations are incrementally usedto determine width and spacing. There are several problems with such anapproach. First, the expand and shrink operation can give correct widthresults only for shapes consisting of axis parallel edges. Once an acuteangle is present the results become incorrect. In addition, the expandand shrink operation is simple only in the case of convex shapes. Forgeneral non-convex shapes, even orthogonal ones, the expand and shrinkoperation is difficult and rather expensive in terms of computationaltime. Furthermore expand and shrink operations work only for givenconstant amounts and, therefore, many calls to these functions aretypically required for standard shapes. As a result, the checking ofdimension dependent rules becomes very cumbersome and time consuming.

One approach to checking spacing dependent rules is to represent a rulein a discrete form given by a small number of “buckets.” “Buckets” arerule implementations based on predefined numeric values or ranges ofpredefined numeric values. For example, buckets for spacing may mandatethat a space be greater than a dimension S if at least one line has awidth greater than a value W. In another example, a space is greaterthan or equal to a dimension S if both lines are greater than a value W.Using the expand/shrink approach to check this type rule is cumbersomeand time consuming. Checking width-dependent spacing rules given in afunction form (i.e., non-step or non-bucketed) would be even morecumbersome (if at all possible) by employing such methods. For example,it is not known how to implement a width-dependent rule that mandatesthat the spacing between two neighboring shapes must be 2× the maximumwidth of one of the shapes minus 10 units.

In addition to the above problems, use of buckets leads to IC designsthat are hard to manufacture. In particular, there are two problems thatresult from the IC design rule implementation using buckets. The firstproblem is based on the premise that design rules are established priorto the creation of a manufacturable process, and thus, the design rulesrepresent assumptions and commitments of the process made during design.Typically, however, process constraints usually deviate by some amountupon reaching manufacturing. Therefore, a design rule legal layout maybe outside the process window capability of the manufacturing process.Avoiding this problem infers that all of a specific “bucket” lies withinthe manufacturing process capability, which leads to the second problemwhere productivity is “left on the table.” In particular, the “bucketed”design rules motivate the designer to use the limit provided rather thanwhat is optimal (assuming the process does not follow the same functionas the buckets). In particular, designers actually make calculationsbased on the bucket specifications to determine which size wires to userather than using the size wire that optimizes their functionality andperformance requirements. The end results lead to a non-optimal ICdesign.

Another problem relative to DRC is that design rules capture diversephysical phenomena, each of which may require a slightly differentdefinition of width and spacing as long as the definition can be treatedin a consistent manner. For example in certain cases a shape may need tobe evaluated as “thin” as possible, while in other cases it may need tobe evaluated as “fat” as possible. Currently, no mechanism exists forapplying different definitions of width and spacing for DRC.

In view of the foregoing, there is a need in the art for a way to modelan IC design that allows for dimension-dependent design rule checkingregardless of shape. It would also be advantageous to be able toimplement different definitions of width and spacing.

SUMMARY OF INVENTION

The invention provides a method, system and program product to model anIC design to include dimensions such as a local width and spacing of ICshapes in a consistent fashion. In particular, the invention uses a corepart of Voronoi diagrams to partition edges of a shape into intervalsand assigns at least one dimension to each interval such as a localwidth and spacing. Dimension assignment can be made as any desirabledefinition set for width and spacing, e.g., numerical values orcontinuous dimension-dependent design rules. Design rule checking fordimension-dependent spacing rules given in any arbitrary functional formof width and spacing is possible. Application of the invention can bemade anywhere the width and spacing of VLSI shapes play a role, e.g.,relative to a single edge, a neighboring edges, a neighboring shapes,and/or for edges in more than one layer of the IC design.

A first aspect of the invention is directed to a method of modeling foruse with an integrated circuit (IC) design, the method comprising thesteps of: partitioning an edge of a shape in the IC design into aplurality of intervals; and assigning at least one dimension to eachinterval.

A second aspect of the invention is directed to an integrated circuit(IC) modeling system comprising: means for partitioning an edge of ashape in the IC design into a plurality of intervals; and means forassigning at least one dimension to each interval.

A third aspect of the invention is directed to a computer programproduct comprising a computer useable medium having computer readableprogram code embodied therein for modeling an integrated circuit, theprogram product comprising: program code configured to partition an edgeof a shape in the IC design into a plurality of intervals; and programcode configured to assign at least one dimension to each interval.

A fourth aspect of the invention is directed to an integrated circuit(IC) check rule evaluation system comprising: means for partitioning anedge of a shape in the IC design into a plurality of intervals, thepartitioning means including: means for generating a core Voronoidiagram for the shape using a first metric, and means for partitioningthe edge based on the core Voronoi diagram; means for assigning at leastone dimension to each interval using a second metric; and means forusing the at least one dimension to evaluate a check rule.

The foregoing and other features of the invention will be apparent fromthe following more particular description of embodiments of theinvention.

BRIEF DESCRIPTION OF DRAWINGS

The embodiments of this invention will be described in detail, withreference to the following figures, wherein like designations denotelike elements, and wherein:

FIG. 1 shows a simplified example of a Voronoi diagram.

FIG. 2A shows an exterior Voronoi diagram for a set of polygons usingthe L_(∞) metric.

FIG. 2B shows an interior Voronoi diagram for a polygon using the L_(∞)metric.

FIG. 3 shows an interior Voronoi diagram for an acute polygon using theEuclidean metric.

FIG. 4 shows an interior Voronoi diagram for the acute polygon of FIG. 3using the L_(∞) metric.

FIGS. 5A-5B show illustrations for description of the L_(∞) metric.

FIG. 6 shows a block diagram of a modeling system according to theinvention.

FIG. 7 shows a flow diagram of operation of the modeling system of FIG.6.

FIGS. 8A-8E show illustrative implementations of the method of FIG. 7relative to the acute polygon of FIG. 3.

FIG. 9A shows illustrative local widths and spacings for the shapes ofFIGS. 2A and 2B.

FIGS. 9B-9C show illustrative implementation of the method of FIG. 7relative to the set of polygons and polygon of FIGS. 2A and 2B,respectively.

FIG. 9D shows a detail of a polygon with a thin neck caused by convcavevertices.

FIGS. 10A-10D show illustrative edge arrangements includingnon-orthogonal angles.

FIG. 11 shows the shape of FIG. 4 including partitioning according tothe L_(∞) metric.

FIG. 12 shows a detail of polygon having a concave vertex.

FIG. 13 shows the shape of FIG. 4 partitioned using L_(∞) metric andassigned dimensions using the Euclidean metric.

FIGS. 14A-14F show the shape of FIGS. 2B and 9C for narrowerpartitioning.

DETAILED DESCRIPTION

For purposes of clarity only, the following description includes thefollowing sections: I. Overview, II. General Definitions, III. SystemOverview, IV. Methodology, and V. Conclusion.

I. Overview

IC design rules and computer-aided design (CAD) tools normally work withboundaries of IC shapes. The invention leverages this fact bypartitioning an edge of a shape into a plurality of intervals. Eachinterval is then assigned a dimension, including in one embodiment alocal width and a local spacing, based on discrete neighboring geometryas derived from a local Voronoi diagram in the interior and/or exteriorof the shape. In other words, a local width and local spacing can bemapped to an edge of a shape. As a result, every boundary point of ashape may be assigned a unique width label and a unique spacing label.

A definition set determines how an edge is partitioned and how width andspacing are assigned for an edge. Definition sets may vary depending ondesign rules. Accordingly, the assignments of width/spacing can reflectthe nature of the design rule of interest and need not be the same forall rules. In addition, each interval can have a constant width/spacingvalue or it can be assigned a function such as the distance from anotherboundary/corner, a factor of another dimension or other function. Oncewidths and spacings are obtained they can be compared against each otherto check any kind of relation between them, and, in particular, can bechecked for compliance with continuous dimension-dependent design rules.

II. General Definitions

As noted above, the invention implements Voronoi diagrams to determinedimensions, i.e., local widths and spacings, of shapes. A “Voronoidiagram” may take a variety of forms depending on the structure to whichit is applied. In the simplest example, referring to FIG. 1, a “Voronoidiagram” 8 for a set of sites (points) 10 a-10 d includes all pointsthat are closer to a corresponding site, e.g., 10 a, than to any othersite 10 b-10 d. The resulting Voronoi diagram 8 includes a collection ofregions 12 a-12 d, called “Voronoi cells,” that divide up the plane inwhich sites 10 a-10 d sit, i.e., the plane of the page. Each Voronoicell 12 a-12 d is in the shape of a convex polygon (for point sitesonly) having edges that are bisectors of sites 10 a-10 d. Each Voronoicell 12 a-12 d corresponds to, or is owned by, one of sites 10 a-10 d.Again, all points in one cell, e.g., 12 a, are closer to thecorresponding site 10 a than to any other site 10 b-10 d.

FIGS. 2A-2B illustrate an exterior Voronoi diagram 20 and an interiorVoronoi diagram 30 for orthogonal shapes, respectively. FIG. 2Aillustrates a set of disjointed polygonal sites 22A-22F, and FIG. 2Billustrates a polygon 122. FIGS. 3 and 4 illustrate interior Voronoidiagrams 40, 90 for an acute polygon shape 34. As used herein, the term“boundary” shall refer to an outer border or line of a shape, while an“edge” shall refer to a component of the boundary.

As shown in FIG. 2A, an external Voronoi diagram 20 for a set ofdisjoined polygonal sites, i.e., polygons 22A-22F, includes apartitioning of the plane containing polygons 22A-22F into Voronoi cells24A-24F. Each Voronoi cell, e.g, 24A, for a polygon 22A includes a locusof points closer to polygon 22A than to any other polygon 22B-22F. Thatis, it includes bisectors of adjacent polygons 22B-22F (others notshown). A Voronoi cell of a site s, e.g., polygon 22A, is denoted asreg(s) and polygon 22A is referred to as the owner of reg(s). A portion23 of Voronoi diagram 20 that borders two Voronoi cells 24A and 24B isreferred to as a “Voronoi edge,” and includes portions of bisectorsbetween the owners of cells. A point 26 where three or more Voronoiedges 23 meet is called a “Voronoi vertex.” Dashed lines indicatepartitioning of polygons 22A-22F such that each boundary, e.g., 28A, ofa polygon 22A has a corresponding portion 23 of Voronoi diagram 20.

Referring to FIGS. 2B, 3 and 4, an interior Voronoi diagram 30, 40, 90on an interior of a shape 34 (polygon 122 in FIG. 2B) is referred to asa “medial axis.” Formally, the “medial axis” is the locus of points [q]internal to a polygon such that there are at least two points on theobject's boundary that are equidistant from [q] and are closest to [q].

The above-described Voronoi diagrams of FIGS. 1 and 3 are illustrated asbased on the Euclidean metric. That is, Voronoi distances are based onthe Euclidean metric. The invention, as will be described further below,may also implement Voronoi diagrams based on an L_(∞) (L-infinity)metric. Referring to FIGS. 5A-5B, in the L_(∞) metric, the distancebetween two points (FIG. 5A) p=(x_(p), y_(p)) and q=(x_(q), y_(q)) isthe maximum of the horizontal distance and the vertical distance betweenp and q, i.e.,d(p,q)=max [|x _(p) −x _(q) |,|y _(p) −y _(q)|].

Intuitively, the L_(∞) distance is the size of the smallest squaretouching p and q. The L_(∞) distance between any two points is less thanor equal to the Euclidean distance between the points. Further, in theL_(∞) metric, the distance between a point p and a line l (FIG. 5B) isd(p,l)=min [d(p,q),∀q□l]. The L_(∞) bisector of two polygonal elements(points or lines) is the locus of points at equal L_(∞) distance fromthe two elements.

Returning to FIG. 4, medial axis 90 of shape 34 is illustrated as basedon the L_(∞) metric. (Medial axis 30 in FIG. 2B is also based on theL_(∞) metric). As easily discerned by comparing FIGS. 3 and 4, the useof the L_(∞) metric simplifies Voronoi diagram 90 of polygonal objectsand makes it simpler to compute. The L Voronoi diagrams are a “skeleton”of straight-line segments having linear combinational complexity. Whilemethodology of the invention will be described based on one or the othermetric, it should be recognized that the concepts and functioning of theinvention are the same regardless of the metric used, and the inventionshould not be limited to any particular metric other than as set forthin the attached claims.

Further explanation of Voronoi diagrams and their application tocritical area determination can be found in U.S. Pat. Nos. 6,317,859 and6,178,539, which are hereby incorporated by reference for all purposes.See also, E. Papadopoulou et al., “The L_(∞) Voronoi Diagram of Segmentsand VLSI Applications,” International Journal of Computational Geometryand Applications, Vol. 11, No. 5, 2001, 503-528.

Returning to FIGS. 2A, 2B, 3 and 4, a “core” 50 (indicated by thickerline) of a Voronoi diagram 30, 40, 90 is the portion remaining afterexcluding “uninteresting portions.” Typically, “uninteresting portions”(lighter lines) are portions of Voronoi edges coupled to a boundary 52(FIGS. 2B, 3 and 4) of the shape, e.g., bisectors 54 between adjacentedges. In the case of IC shapes with acute angles (i.e., concavevertices), as shown in FIGS. 3 and 4, “uninteresting” can be a portionof a bisector 54 coupled to an acute angle 56 at a certain distance fromacute angle 56. What is excluded from core 50 can be flexible andapplication dependent. For simplicity, core 50 shall include all Voronoiedges 23 that are not coupled to boundary 52 of shape 34, i.e., allbisectors between non-adjacent edges and non-degenerate bisectors. A“degenerate bisector” is one between two collinear horizontal/verticaledges. However, it should be clear that core 50 is the “interesting”subset of a Voronoi diagram 30, 40, 90 where the “interesting”classification can vary for each application.

A “spot defect” is caused by particles such as dust or othercontaminants in materials and equipment and are classified as two types:“extra material” defects causing a short between different conductingregions, e.g., 22A-22F of FIG. 2A, and “missing material” defectscausing an open, e.g., in polygon 122 of FIG. 2B. In other words, a“short” is a defect creating a bridge with some other edge in theexterior of a shape while an “open” is a defect creating a void in theinterior of a shape. Referring to FIG. 3, a spot defect may be modeledas a “core element” 60 in the form of a circle (Euclidean metric only)or a square (L_(∞) metric in FIGS. 2A, 2B and 4). That is, a “coreelement” 60 can be represented by a circle or a square depending on themetric used. Since, in reality, spot defects have any kind of shape, thesquare (L_(∞) metric) defect model is good for most purposes. The term“core disk” will be used to refer to the circles of the Euclideanmetric, and “core square” will be used to refer to the square of the Lmetric, and the term “core element” is generic to both.

A “core element” 60 touches a boundary 52 in at least two points 64, andhas a center referred to as a “core point” 62, which is a member of core50 for a shape, e.g., polygon 122 in FIG. 2B. Each core point 62 isweighted with twice its distance from boundary 52 of a shape, i.e., thediameter of it's core element. That is, each core point 62 is weightedwith twice the radius of an associated core element 60. In the Euclideanmetric, there is at most one core disk touching a boundary point exceptfrom concave vertices of the shape that can be touched by multiple coreelements 60. In contrast, in the L₂₈ metric, there may be more than onecore square touching a boundary point. See, for example, point p in FIG.12. In particular, in the L_(∞) metric, where core squares areaxis-parallel squares, boundary points along axis parallel boundaryedges can be touched by more than one core square. The “radius of asquare” is defined as half the size of its side. The above-describedweighting provides a mechanism to map dimensions (width or spacing)information of a Voronoi diagram (interior or exterior) to the boundaryof a shape.

A “core element” 60 may also be called a “minimal open” where core point62 is in the interior of a shape because any shrinking of core element60 (i.e., of the wire formed by the shape) of ∈>0 makes it such thatcore element 60 stops overlapping any boundary point 64, thus ceasing tocreate an open circuit. ∈is a positive number arbitrarily small, and toshrink ∈ means to move the edges of a defect towards an interior of thedefect by a distance ∈. Similarly, referring to FIG. 2A, a “coreelement” 60 may also be called a “minimal short” where core point 62 isexternal of a shape, e.g., polygons 22A, 22B, because any shrinkage ofcore element 60 (i.e., spacing between wires) of ∈>0 (same definition asabove) makes it such that core element 60 stops overlapping any boundarypoint 64 of a shape 22A, 22B, thus ceasing creation of a short circuit.

A “definition set” is one or more definitions that allow forpartitioning of an edge of a shape and assigning of at least onedimension (either as a constant value or a function) to each interval.

Other definitions will be provided, as necessary in the description thatfollows.

III. System Overview

With reference to the accompanying drawings, FIG. 6 shows a blockdiagram of a modeling system 100 in accordance with the invention.Modeling system 100 includes a memory 112, a processing unit (PU) 114,input/output devices (I/O) 116 and a bus 118. A database 120 may also beprovided for storage of data relative to processing tasks. Memory 112includes a program product 122 that, when executed by PU 114, comprisesvarious functional capabilities described in further detail below.Memory 112 (and database 120) may comprise any known type of datastorage system and/or transmission media, including magnetic media,optical media, random access memory (RAM), read only memory (ROM), adata object, etc. Moreover, memory 112 (and database 120) may re-side ata single physical location comprising one or more types of data storage,or be distributed across a plurality of physical systems. PU 114 maylikewise comprise a single processing unit, or a plurality of processingunits distributed across one or more locations. I/O 116 may comprise anyknown type of input/output device including a network system, modem,keyboard, mouse, scanner, voice recognition system, CRT, printer, discdrives, etc. Additional components, such as cache memory, communicationsystems, system software, etc., may also be incorporated into system100.

As shown in FIG. 6, program product 122 may include an intervalpartitioner 123 having a core Voronoi diagram generator 124 and apartition generator 126, and a dimension assigner 128. At least onedefinition set 130 may be provided for use by system 100, as will bedescribed below. A design rule checker 132 may also be provided as partof system 100, or it may be configured as a separate system. Othersystem components 134 include any other program product necessary toimplement the invention and not otherwise described herein, e.g., userinterfaces, communications, etc.

An IC design 140 is provided to modeling system 100 and is modeledaccording to the following methodology. It should be recognized thatmodeling system 100 may be provided as a stand-alone system or as partof a larger IC design system as now known or later developed.

IV. Methodology

Referring to FIG. 7, a flow diagram of operation of modeling system 100will now be described. The processing of FIG. 7 will be described,first, relative to an (arbitrary acute-polygon) shape 34 as originallyshown in FIGS. 3 and 4, and also shown in FIGS. 8A-8D. Shape 34 is anun-likely occurrence in a VLSI design, but facilitates a goodunderstanding of the overall methodology. To further facilitate a goodunderstanding, the process description relative to shape 34 will be maderelative to the Euclidean metric. Subsequently, the processing of FIG. 7will be described relative to FIGS. 9A-9C, which mimic FIGS. 2A-2B,respectively, and represent more likely VLSI design possibilities. Inthis latter description, use of the L_(∞) metric will be explained.

In either case, partitioning and assignment of dimensions to a boundaryof a shape can be based on a definition set 130 (FIG. 6). A definitionset for dimensions (width and spacing) may vary depending onapplication. In addition, the definition set may require assignment ofan actual figure or be a function dependent on some other dimension orcharacteristic. In view of the foregoing, the definition sets discussedbelow are meant to be illustrative only.

As an overview, the methodology includes: step S1, generate a coreVoronoi diagram; step S2, partition edges into intervals (width and/orspacing); step S3, assign dimensions; and step S4, conduct design rulechecking. For purposes of clarity, partitioning and assigning dimensionswill be described together in a single section. That section includessub-sections relating to the different metrics, shape configuration andspecial situations.

1. Generate Core Voronoi Diagram

Referring to FIG. 8A, in a first step S1 (FIG. 7), a core 100, 102 foran interior and/or exterior Voronoi diagram 40 (i.e., medial axis) and92, respectively, are generated for shapes of a given layer A of an ICby core Voronoi diagram generator 124 (FIG. 6). Step S1 may be segmentedinto step S1A for generating a Voronoi diagram, and step S1B fordetermining a core of the Voronoi diagram. Core Voronoi diagrams 100,102 are generated as based on the Euclidean metric. Generation ofVoronoi diagrams 40, 92 can be completed, for example, according to thealgorithm described in U.S. Pat. No. 6,317,859, previously incorporatedby reference. Generation of a core 100, 102 can be accomplishedaccording to a set of user-defined rules to select only interestingportions of the respective Voronoi diagram. For example, as noted above,“uninteresting portions” (lighter lines) may be portions of Voronoiedges coupled to a boundary 52 of the shape, e.g., bisectors 54 betweenadjacent edges. In the case of IC shapes with acute angles,“uninteresting” can be a portion of a bisector 54 coupled to an acuteangle 56 at a certain distance from acute angle 56. Once again, what isexcluded from core 100, 102 can be flexible and application dependent.

FIGS. 2A and 2B also show a core 50 for an exterior and interior Voronoidiagram, respectively. However, these Voronoi diagrams are generatedbased on the L_(∞) metric. In terms of FIG. 2B, “uninteresting portions”(lighter lines) may be portions of Voronoi edges coupled to a boundary52 of the shape, e.g., bisectors 54 between adjacent edges.

2. Partitioning into Intervals and Assigning Dimensions

A. Arbitrarily (Acute) Shaped Polygon with Euclidean Metric

Turning to FIGS. 8A-8D, in conjunction with FIG. 7, shape 34 of FIG. 3is shown for description of the process. In addition, another shape 94is provided for discussion of an exterior Voronoi diagram 92.

For arbitrarily shaped polygons, an illustrative definition set may be:

Definition 1 (Arbitrary case): The width of a point p on the boundary ofshape P is the size of the smallest core-disk touching p in the interiorof shape P. If there is no core-disk touching p, then p gets assignedthe width of the nearest boundary point touched by a core-disk as theboundary of shape P is followed in a particular direction (clockwise orcounterclockwise).

Definition 2 (Arbitrary case): The spacing of a point p on the boundaryof shape P is the size of the smallest core-disk touching p in theexterior of shape P. If there is no core-disk touching p then p getsassigned the spacing of the nearest boundary point touched by a coredisk as the boundary of shape P is followed in a particular direction(clockwise or counterclockwise).

In a second step S2 (FIG. 7), each edge of each shape is partitionedinto at least one interval by partition generator 126 (FIG. 6). In oneembodiment, this step includes partitioning each edge into widthintervals using an interior core Voronoi diagram 100 and spacingintervals using an exterior core Voronoi diagram 102. Referring to FIG.8B, partitioning into dimension intervals, in this case in the form ofwidth intervals, w1-w26, is shown.

In one embodiment, partitioning is conducted by projecting (dashedprojections 104)(only some shown) for a vertex v of core 100(hereinafter “core vertex”) to a corresponding boundary projection point106 (only some shown) of shape 34. In this case, partitioning rules canbe applied to address specific situations. One example set ofpartitioning rules are as follows:

a) For each core vertex v of a core bisector bisecting edges e1 and e2,project core vertex v to both edges e1 and e2 such that each projectionis perpendicular to the respective edge. Referring to FIG. 8B, anexample core vertex of a core bisector 100A bisecting edges 52A, 52B iscore vertex v1. Projections 104A, 104B for core vertex v1 to both edges52A, 52B are shown such that each projection 104A, 104B is perpendicularto the respective edge 52A, 52B. The result is width intervals w15 andw16 result on edge 52A and intervals w4 and w6 result on edge 52B.

b) For each core vertex v of a core bisector bisecting an edge e1 (oredges) and a concave vertex of a shape, project the core vertexperpendicular to edge e1 (or edges). A “concave vertex” is a vertex forwhich a line segment that connects points of edges forming the vertex isentirely outside of the shape, i.e., a vertex forming an angle greaterthan 180°.

Referring to FIG. 8B, an example core vertex v2 of a core bisector 100Bthat bisects an edge 52C and a concave vertex w7 of shape 34 is shown.(Note, concave vertices are labeled as intervals because each concavevertex represents an interval, as will be described in greater detailbelow.) In this case, a projection 104C is made from core vertex v2perpendicular to edge 52C and edge 52C is partitioned accordingly, i.e.,into width intervals w12, w13 based on projection 104C. Similarly, acore vertex v3 of a core bisector 100C that bisects an edge 52A andconcave vertex w7 is shown. Projection 104D is made from core vertex v3perpendicular to edge 52A to form intervals w14 and w15. Assignment of adimension, as will be described below, for width intervals w12 and w13are based on core vertex v2, and for width intervals w14 and w15 isbased on the weighting of core vertex v3.

c) Each concave vertex is its own interval. In FIG. 8B, concave verticesare labeled with intervals w5, w7 and w23.

Returning to FIG. 8B, projections 104 define a list of intervals onboundary 52 of the shape. Based on the above projections, intervalsw1-w26 result. It should be recognized that the projection rules can bemodified to suit an application, and the above rules are onlyillustrative.

In an alternative embodiment shown in FIGS. 8C-8D, the partitioning maybe made by generating the core-disk 60 centered at each core vertex v,and determining point(s) where the core disk 60 touches boundary 52 toform points 106. FIG. 8C shows smallest core disks 60 (Euclideancircles) for a variety of core points (not necessarily core vertices) ofshape 34. In the Euclidean metric, there is at most one core-disk 60touching a boundary point 106 except from concave vertices. (In theL_(∞) metric, there is more than one core-disk 60 touching a boundarypoint. Here, the invention may use the smallest core-disk 60 such thatthe smallest possible (narrowest) width/spacing values are assigned.However, a user may choose to use the size of the largest core-diskinstead if the local width of concave vertices is to be ignored.)Referring to FIG. 8D, this embodiment provides the equivalentpartitioning as projecting core vertices to boundary 52, as describedabove.

While the above description has been made relative to width intervals,it should be recognized that this process can be repeated for exteriorcore Voronoi 92 such that spacing intervals are derived. That is, asshown in FIG. 8B, projections from core vertices of core Voronoi 92 aremade to boundary 52 to derive spacing intervals, e.g., s1.Alternatively, as shown in FIG. 8D, core disks 60 can be drawn at eachcore vertex, and the points at which the core disk touch boundary 52 canbe used to derive spacing intervals, e.g., s1.

Next, in step S3, assigning dimensions to each interval is conducted bydimension assigner 128 (FIG. 6) according to a selected definition set130 (FIG. 6). It should be recognized that while the particulardefinition set provided above assigns actual dimensions, a definitionset may assign dimensions as a function, e.g., width is twice the widthof dimension×minus 10 nm. That is, a definition set may include a set ofrules for partitioning and then assign a function. For each point palong an interval, a core point that projects to p, referred to as c(p),defines a dimension. For example, returning to FIG. 8B, a width for anypoint in, for example, intervals w9, w10, w11 is assigned a dimensionequivalent to the weighting of a respective core point, i.e., vertex v4,where the weighting equals the diameter of a core disk centered at v4.This is consistent with Definition 1 above. Turning to interval w6, awidth assigned to a point p1 along that interval has a variable widthgiven by the diameter of a core disk centered at core point c(p1). Thisis also consistent with Definition 1 above. Also according to Definition1, for a point P4 not touched by a core disk, the dimension assigned isthe width of the nearest boundary point touched by a core-disk as theboundary of shape 34 is followed in a particular direction (clockwise orcounterclockwise). Note that any point along intervals w9, w10, w11, thecore point is core vertex v4.

With regard to concave vertices w5, w7 and w23, as noted above, eachconcave vertex is an interval itself. In this case, assignment of adimension is based on a number of core points (or weights of corepoints), i.e., exactly two core points for each of the two adjacentedges, and potentially a number of core points induced by Voronoi edgesbisecting the concave vertex and other concave vertices (if any). In oneembodiment, the dimension assigned is based on the minimum among theweights of these core points. For example, as shown in FIG. 8E, twoconcave vertices A, B can create a very thin neck in a shape. For aconcave vertex A, determine the core point of minimum weight along thecore bisectors induced by core vertex A. For example, in FIG. 8E, a corebisector 100D (between arrows) is induced by core vertices A and B, andvertices A, B are assigned the weight of the depicted core disk 60.

Assignment of spacing dimensions occurs in a similar fashion. Forexample, as shown in FIG. 8B, for a point P2 on edge 52A, the spacing ofthe point would be the weight of a projected core point c(p2), i.e., thelargest core-disk touching point P2, i.e., twice the distance from corepoint c(p2) to point P2. If no core-disk touched a point, e.g. point P3,then the spacing is assigned the spacing of the nearest boundary pointtouched by a core disk.

B. Orthogonally (VLSI) Shaped Polygon with L_(∞) Metric

A description of the methodology applied to an orthogonal shape usingthe L metric will now be made with reference to FIGS. 2A, 2B, 9B, 9C and9D. The methodology for an orthogonally shaped polygon such as thatshown originally in FIGS. 2A-2B is identical to that for an arbitrarypolygon. However, the definition set may be altered to accommodate thedifferent shapes, as will be described below. FIG. 9A shows withdouble-ended arrows illustrative important local widths and spacings forthe group of shapes 22A-22F and 122 shown in FIGS. 2A and 2B,respectively. FIGS. 2A and 2B illustrate core Voronoi diagrams 50, andFIGS. 9B and 9C illustrate use of core Voronoi diagrams 50 to partitionand assign dimensions, as will be described below.

As noted above, the following description will use the L_(∞) metricrather than the Euclidean metric. The Voronoi diagram for the L_(∞)metric is much easier to compute in practice than a Euclidean one.Moreover, a vast majority of VLSI shapes include an axis parallel edgeor edges of slope ±1 (ortho-45 shapes). In this case, the L_(∞) metricis very appropriate and simple to use. Where a general IC designcontains an edge in more orientations than ortho-45 shapes, anapproximation to an ortho-45 shape can be easily made to compute theL_(∞) metric Voronoi diagram.

Interval size can be determined based on the definition set thatprovides a “partitioning profile.” For a larger partitioning, in thecase of an orthogonal polygon(s), as shown in FIGS. 9B-9C, a definitionset may be based on a “largest empty disk (square)” partitioningprofile. Note that the following definitions are derived from Definition1 and 2 by taking into account that a core square touching an orthogonaledge in the L metric need not be unique as in the Euclidean case. Adefinition set is as follows:

Definition 3 (Orthogonal case): The width of any boundary point p alongan edge e of a shape P is the size of the largest square touching p(along e) that is entirely contained in the interior of P.

Definition 4 (Orthogonal case): The spacing of any boundary point palong an edge e of a shape P is the size of the largest square touchingp (along e) that lies entirely in the free space, i.e., it does notintersect P or any other shape.

Concave corners present a special case similar to the Euclidean case ofconcave vertices. In particular, concave corners have a width/spacingjust as any other point p on the incident edges, and also have a cornerwidth/spacing. Accordingly, the following definitions are presented toaddress concave corners:

Definition 5 (Orthogonal case): The corner width of a concave cornerpoint p of a shape P is the size of the largest square cornered at pentirely contained in the interior of P. The width of concave corner pis the smallest among the widths of the two edges incident to p and thecorner width of p.

Definition 6 (Orthogonal case): The corner spacing of a concave cornerpoint p of a shape P is the size of the largest square cornered at pentirely contained in the free space. The spacing of concave corner p isthe smallest among the spacings of the two edges incident to p and thecorner spacing of p.

(It should be recognized that the definition set may be altered to formsmaller intervals and smaller dimensions by using a smallest possiblecore square partitioning profile for each vertex to determine intervalpartitioning and dimension assignment. This results in more intervalsfor each edge.)Returning to the methodology, in second step S2 (FIG. 7),partitioning of each edge of each shape into dimension intervals isconducted by partition generator 126 (FIG. 6). In one embodiment, thisstep includes partitioning into width intervals using an interior coreVoronoi diagram 50 (FIG. 2B) and partitioning into spacing intervalsusing an exterior core Voronoi diagram 50 (FIG. 2A).

Returning to FIG. 2A-2B, partitioning into dimension intervals fororthogonally shaped polygons includes evaluating or scanning a Voronoicell of an edge, e.g., edge e, to identify Voronoi core vertices vinduced by that edge e. For example, referring to FIG. 2B, edge e ofpolygon 70 has five Voronoi vertices v1, v2, v3, v4, v5 adjacentthereto, and, as shown in FIG. 2A, edge f of polygon 22A has threeVoronoi vertices v4, v5, v6 adjacent thereto. For each Voronoi vertex vencountered, as shown in FIGS. 2A, 2B, a core square 60 centered at theVoronoi vertex v is generated. Since the Voronoi diagrams are generatedusing the L_(∞) metric, core elements are square. The core square has aside length twice the weight of the Voronoi vertex, i.e., twice theweight of the core point identical to the Voronoi vertex. Note that thisstep is equivalent to projecting core vertex v on the boundary of ashape along directions +1 and/or −1. Whether the direction +1 or −1 isused depends on the slope of the boundary edge.

In one embodiment, derivation of intervals can proceed based on adesired partitioning profile. This is similar to the simplified processpresented relative to arbitrary shapes. In this embodiment, for example,partitioning can be conducted such that the intervals are as large aspossible (coarser partitioning profile) or as small as possible(narrow/fine partitioning profile). In the former case, a largest emptycore square possible at each vertex is evaluated to determine intervalpartitioning. For example, referring to FIG. 9B, for edge f, threespacing intervals s1, s2, s3 are generated because three largest squares168, 170, 172 along edge f are possible (for core vertices v4, v5, v6 inFIG. 2A). Similarly, referring to FIG. 9C, for edge e, three widthintervals w1, w2, w3 are generated because three largest core squares162, 164, 166 (for core vertices v1, v3 and v5 in FIG. 2B) along edge eof the shape are possible. In some cases, some core squares may overlapwith each other because a core square touches an axis parallel boundaryedge with its whole side and not only with its corner. See, for example,core square 177 and core square 164 in FIG. 9C. In one embodiment, forany overlapping portions of a core square, only the portion of largestweighting is maintained, and portions of a smaller weighting areeliminated. Alternatively, other user-defined rules may be implementedto address overlapping core squares. In FIG. 9C, core squares 177, 178for vertices v2 and v4 do not provide the largest core squares at thevertices and, hence, they are eliminated. The above-described process isrepeated for both the interior (for width) face and exterior (forspacing) face of each edge.

Next, in step S3, assigning actual or function dimensions to eachinterval is conducted by dimension assigner 128 (FIG. 6). In oneembodiment, step S3 includes implementation of a definition set 130(FIG. 6) to assign dimensions to each interval. As noted above,according to the invention, a definition set for dimensions (width andspacing) may vary depending on application. In addition, the definitionset may require assignment of an actual figure or be a functiondependent on some other dimension or characteristic. It should berecognized that the particular partitioning profile used to partitioneach edge into intervals does not require implementation of acorresponding dimension assignment profile. For example, a user maypartition an edge based on a largest empty core square partitioningprofile to attain larger intervals, and then assign dimensions based ona definition set that assigns the smallest possible dimension.

Referring to FIG. 9B, for edge f of polygon 22A, any point within thethree spacing intervals s1, s2, s3 is each assigned the dimension oftheir respective three largest squares 168, 170, 172 according toDefinition 4. That is, any point p within an interval is assigned theweight of its unique core point c(p), referred to as the core point thatprojects to p. For any p that is part of an axis parallel edge, c(p) isthe center of the largest core square touching p. Note that thedimensions of squares 168 and 172 are limited by the horizontaldimension, while square 170 is limited by the vertical dimension.Referring to FIG. 9C, for edge e, any point p within the three widthintervals w1, w2, w3 are each assigned the width of the respectivelargest core square, i.e., core point that projects to p, according toDefinition 3. Note that the dimensions of squares 162 and 166 arelimited by the horizontal dimension, while square 164 is limited by thevertical dimension.

With regard to a corner width, as shown in FIG. 9C, the corner width ofa point p is the size of largest square that is cornered at p andentirely contained in the interior of polygon according to Definition 5.In addition, the width of corner p is the smallest among the widths ofthe two edges g, h incident to p and the corner width of p. With regardto corner spacing, as shown in FIG. 9B, the corner spacing of a cornerpoint p of polygon 22A is the size of the largest square 178 cornered atp entirely contained in the free space according to Definition 6. Inaddition, the spacing of corner p is the smallest among the spacings ofthe two edges f, i incident to p, i.e., square 172 or 176, and thecorner spacing of p, i.e., the size of square 178 at the corner of p.Note that the largest empty square 178 cornered at a corner p gives theL_(∞) nearest neighbor to corner p that may not be the same as theEuclidean nearest neighbor. The difference, however, between the two issmall and negligible in practice. Once the L_(∞) nearest neighbor to pis identified, the numeric distance can be reported in the ordinary(Euclidean) manner, e.g., 160A instead of 160B. Another example ofcorner width determination is shown in FIG. 9D. In this case, anorthogonal shape includes three core squares 360A-C (dashed boxes) at aconcave corner p. In this case, the core square 360B would be used todefine the width of corner p.

It should also be recognized that each interval may be assigned afunction that determines its dimension(s) rather than a numerical valuebased on its associated core square. For example, an interval s1 in FIG.9B may be given a function that assigns its width as 2 times the size ofthe width of polygon 22B minus 10 nm.

1) Handling of Ortho-45° Edges

Referring to FIGS. 10A-10D, various arrangements of widths for shapescontaining 45° edges are illustrated. The methodology is the same asdescribed above. Portions of a medial axis 250, 252 not included in thecore are shown with dashed lines 202.

FIG. 10A illustrates core squares 260A-D for core 250 corresponding to a45° line. In this case, partitioning is based on the largest coresquares 260A and 260D along a boundary edge, which results in twointervals.

As shown in FIG. 10B, for intervals corresponding to two parallel 45°lines, the invention may use the diameter of a core square 200. In thecase of two parallel 45° lines, the Euclidean and L_(∞) metric reachtheir greatest difference in values. To simulate Euclidean distance, thesize of a core square, in this case, can be defined to be the length ofthe diagonal of the core-square. Note that the length of the diagonalequals the Euclidean distance between the two parallel 45° lines. In allremaining cases, size is determined by the length of the side of thecorresponding core square. FIGS. 10B and 10C also illustrate theadvantages of being able to select a core, i.e., based on what isinteresting and uninteresting. In FIG. 10B, a bisector 202 of adjacentedges j, k is excluded from core 250. Thus, the same width w1 may beassigned to the whole 45° edge k, even in the portion close to the acuteangle. In FIG. 10C, a portion 204 of bisector 202 incident to the acuteangle is included in core 252, and thus three intervals w1, w2 and w3are generated, where w3 is assigned the constant value of the smallvertical arrow 206. Note also that once intervals w2 and w3 areobtained, any reasonable numeric value approximating the Euclideanmetric may be assigned, if desirable.

FIG. 10D illustrates the case of two perpendicular 45° edges forming a90° angle, which correspond to a rotated rectangle. This case is handledsimilarly to that of FIG. 10A.

2) Arbitrarily (Acute) Shaped Polygon with L_(∞) Metric

Referring to FIG. 11, the arbitrary shape 34 of FIG. 4 is shownincluding partitioning according to the L_(∞) metric. Where the L_(∞)metric is applied to non-orthogonal shapes, a definition set may be asfollows:

Definition 7 (Arbitrary case): The width of any boundary point p along aboundary of shape P is the size of the largest core square touching p inthe interior of shape P. If there is no core-square touching p, then pgets assigned the width of the nearest boundary point touched by a coresquare.

Definition 8 (Arbitrary case): The spacing of any boundary point p alonga boundary of shape P is the size of the largest core square touching pin the exterior of shape P. If there is no core-square touching p, thenp gets assigned the spacing of the nearest boundary point touched by acore square.

As noted above, special care must be taken for concave corners. Inparticular, concave corners represent an interval by themselves. Thatis, they have a width/spacing just as any other point p in an edge, andalso have a corner width/spacing. Accordingly, the following definitionsare presented to address corners:

Definition 9 (Arbitrary case): The corner width of a concave cornerpoint p of a shape P is the size of the smallest among all core squarecornered at p.

Referring to FIG. 12, there may be at most 3 core squares cornered at aconcave corner p depending on the slopes of the incident edges. In theorthogonal case, there are exactly 3 core squares cornered at p.

Definition 10 (Arbitrary case): The corner spacing of a concave cornerpoint p of a shape P is the size of the smallest core square cornered atp entirely contained in the free space.

3) Improved Accuracy: Combination L_(∞) Metric and Euclidean Metric:

Because shapes are in their majority axis parallel and because the L_(∞)Voronoi diagram is easier to compute, the invention preferably uses theL_(∞) metric. In an alternative embodiment, if more accuracy is desired,an approximation to the Euclidean metric can be implemented by, as shownin FIG. 13:First, partitioning the boundary of a shape into intervalsaccording to the L_(∞) metric, i.e., the definition based on the largestsquare centered along the L_(∞) core as given in Definitions 5-6.Second, the Euclidean metric can be used to assign dimension. Thisprocedure can be completed as follows: Consider a core square D centeredat core point c(p). Points p1 and p2 are neighbors of point p, and viceversa. Similarly edges e1 and e2 are neighbors of point p. Instead ofassigning the side of core square D as the width of p, Euclidean basedmetrics may be used. For example, the size of a circle defined by pointp, edge e1 and edge e2 may be used. Alternatively, the size of a circlecentered at core point c(p), or the distance between point p and edge e2(shown by double ended arrow), or the distance between point p and edgee1 (shown by double ended arrow) may be used.

As another example, as shown in FIG. 13, points p3 and p4 are neighbors.Instead of assigning the side of core square D′ as the width of p3 andp4, the Euclidean based distance between point p4 and edge e1, or thesize of a circle centered at core point c(p4), or the diagonal of coresquare D′, etc., may be used.

4) Fine and Narrow Partitioning

In certain applications the focus of width and spacing is to evaluate ashape and the spacing around a shape as “narrow” and as “thin” aspossible. In particular, in the area of VLSI yield and critical areacalculations, the notion of shorts and opens is widely used. As notedabove in the definition section, a “spot defect” causes a short or anopen where a “short” is a defect creating a bridge with some other edgein the exterior of a shape and an “open” is a defect creating a bridgein the interior of a shape. In addition, a defect may be modeled as acore element in the form of a circle or a square.

In order to implement the invention to partition and assign dimensionsin terms of a “narrow” or “thin” evaluation, the following definitionset (for L_(∞) and Euclidean metric) may be used:

Definition 11: The width of any boundary point p of shape P is theradius of the smallest core element (defect) centered at p causing anopen for shape P. The spacing of the boundary point p is the radius ofthe smallest core element (defect) centered at p that causes a short.

Definition 12: An open is an element totally covering a core elementthat is centered on a core point in the interior of a shape P. A shortis an element totally covering a core element that is centered on a corepoint in the exterior of a shape P.

Returning to the methodology and referring to FIGS. 14A-14E,partitioning of an edge e into width/spacing intervals based onDefinition 11 will now be described. FIG. 14A shows an interior Voronoicell 124A (also denoted reg(e) and shaded) of shape 122 (from FIGS. 2Band 9C). FIG. 14B shows a second (2^(nd)) order Voronoi diagram 390(dashed lines) of shape 122 within Voronoi cell 124A (also denotedreg(e)) that is the Voronoi diagram of shape 122 truncated withinreg(e). The 2nd order Voronoi diagram within Voronoi cell 124A isgenerated by extending in Voronoi cell 124A all bisectors 54 incident toVoronoi cell 124A except those incident to endpoints 62E of a core 50,i.e., except those induced by an edge adjacent to e. The 2nd orderVoronoi diagram for opens within cell 124A is the 2nd order Voronoidiagram of shape 122 within the cell excluding in addition to edge e thetwo edges of shape 122 neighboring edge e. For simplicity, the 2nd orderVoronoi diagram 390 for opens may be referred to as the “2nd orderVoronoi diagram” or the “2nd order Voronoi partitioning within reg(e).”

The 2nd order Voronoi partitioning within reg(e) partitions edge e intointervals w1, w2, w3. Each interval has an “owner,” i.e., an edge orconcave corner or a core Voronoi vertex that induces that interval. InFIG. 14C, intervals and their owners are indicated by double arrows. Thewidth of any point p along an interval w is simply the distance of pfrom the owner of the interval. In case the owner of an interval is acore point as shown in FIG. 14E, the weight of the core point is addedto the derivation of the width, i.e., the width is the size of the coredisk centered at that core point.

FIG. 14D shows the 2nd order Voronoi partitioning of each Voronoi cellof shape 122 as well as the width intervals. FIG. 14F shows the actualwidth values obtained for the 3 intervals of edge e. Note, the top andbottom interval w1, w3 have constant width while the middle interval w2has a variable width equal to the distance of any point p along thatinterval from the horizontal edge e′.

It should be recognized that although the L_(∞) metric has been used inFIGS. 14A-14F, the Euclidean metric may be used when reporting distancesbetween a point along an interval and its owner.

In the orthogonal case under the L_(∞) metric only the width/spacingdefinition of this section is equivalent to the one in the previoussection Definition 9-10, if we always choose the smallest core-squaretouching a point p to derive its width.

3. Design Rule Checking

Returning to FIG. 7, once intervals and associated dimension(s), i.e.,width/spacing, have been assigned, in step S4, data can be used toconduct any design rule checking involving width and spacing usingconventional technology. For example, width and/or spacing dimensionsfor any single edge may be compared to check rules involving the widthand/or spacing dimension of the single edge. Similarly, width and/orspacing dimensions for pairs of neighboring shapes and/or pairs ofneighboring edges may be compared to check rules involving pairs ofneighboring shapes and/or edges.

It should also be recognized that the above invention is not limited toapplication within a layer A of an IC. In an alternative embodiment, forcheck rules involving shapes in more than one layer of an IC, e.g., alayer A and a layer B, a Voronoi diagram for the combined layers can beused. For example, for each edge of layer A, spacing intervals can bederived with edges in layer B using the combined Voronoi diagram. Thespacing intervals can then be used to compare to check rules involvinglayer A and layer B.

V. Conclusion

In the previous discussion, it will be understood that the method stepsdiscussed are performed by a processor, such as PU 114 of system 100,executing instructions of program product 122 stored in memory. It isunderstood that the various devices, modules, mechanisms and systemsdescribed herein may be realized in hardware, software, or a combinationof hardware and software, and may be compartmentalized other than asshown. They may be implemented by any type of computer system or otherapparatus adapted for carrying out the methods described herein. Atypical combination of hardware and software could be a general-purposecomputer system with a computer program that, when loaded and executed,controls the computer system such that it carries out the methodsdescribed herein. Alternatively, a specific use computer, containingspecialized hardware for carrying out one or more of the functionaltasks of the invention could be utilized. The present invention can alsobe embedded in a computer program product, which comprises all thefeatures enabling the implementation of the methods and functionsdescribed herein, and which—when loaded in a computer system—is able tocarry out these methods and functions. Computer program, softwareprogram, program, program product, or software, in the present contextmean any expression, in any language, code or notation, of a set ofinstructions intended to cause a system having an information processingcapability to perform a particular function either directly or after thefollowing: (a) conversion to another language, code or notation; and/or(b) reproduction in a different material form.

While this invention has been described in conjunction with the specificembodiments outlined above, it is evident that many alternatives,modifications and variations will be apparent to those skilled in theart. Accordingly, the embodiments of the invention as set forth aboveare intended to be illustrative, not limiting. Various changes may bemade without departing from the spirit and scope of the invention asdefined in the following claims.

1. A method of modeling for use with an integrated circuit (IC) design,the method comprising the steps of: partitioning an edge of a shape inthe IC design into a plurality of intervals; and assigning at least onedimension to each interval.
 2. The method of claim 1, wherein thepartitioning step includes: generating a core Voronoi diagram for theshape; and partitioning the edge based on the core Voronoi diagram. 3.The method of claim 2, wherein the core Voronoi diagram is generatedbased on the L∞ metric, and the assigning is based on a Euclideanmetric.
 4. The method of claim 2, wherein the partitioning step furtherincludes partitioning the edge based on a core element for each vertexof the core Voronoi diagram.
 5. The method of claim 4, wherein the coreelement is one of a largest possible core element and a smallestpossible core element.
 6. The method of claim 5, wherein in the casethat the core element is the largest possible core element, theintervals are as large as possible, and wherein in the case that thecore element is the smallest possible core element, the intervals are assmall as possible.
 7. The method of claim 1, wherein the at least onedimension includes a width for each interval and a spacing to aneighboring shape for each interval.
 8. The method of claim 1, whereinthe dimension is a function of another dimension.
 9. The method of claim1, further comprising the step of using the at least one dimension toevaluate a check rule.
 10. The method of claim 9, wherein the check ruleinvolves at least one of: a single edge, a pair of neighboring edges,and edges within more than one layer of the IC design.
 11. The method ofclaim 1, wherein each concave vertex of the shape is an interval.
 12. Anintegrated circuit (IC) modeling system comprising: means forpartitioning an edge of a shape in the IC design into a plurality ofintervals; and means for assigning at least one dimension to eachinterval.
 13. The system of claim 12, wherein the partitioning meansincludes: means for generating a core Voronoi diagram for the shape; andmeans for partitioning the edge based on the core Voronoi diagram. 14.The system of claim 13, wherein the partitioning means further includesmeans for partitioning the edge based on a core element for each vertexof the core Voronoi diagram.
 15. The system of claim 14, wherein thecore element is one of a largest possible core element and a smallestpossible core element.
 16. The system of claim 15, wherein in the casethat the core element is the largest possible core element, theintervals are as large as possible, and wherein in the case that thecore element is the smallest possible core element, the intervals are assmall as possible.
 17. The system of claim 12, wherein the at least onedimension includes a width for each interval and a spacing to aneighboring shape for each interval.
 18. The system of claim 12, whereinthe dimension is a function of another dimension.
 19. The system ofclaim 12, further comprising means for using the at least one dimensionto evaluate a check rule.
 20. The system of claim 19, wherein the checkrule involves at least one of: a single edge, a pair of neighboringedges, and edges within more than one layer of the IC design.
 21. Acomputer program product comprising a computer useable medium havingcomputer readable program code embodied therein for modeling anintegrated circuit, the program product comprising: program codeconfigured to partition an edge of a shape in the IC design into aplurality of intervals; and program code configured to assign at leastone dimension to each interval.
 22. The program product of claim 21,wherein the partitioning code includes: program code configured togenerate a core Voronoi diagram for the shape; and program codeconfigured to partition the edge based on the core Voronoi diagram. 23.The program product of claim 22, wherein the partitioning code furtherincludes program code configured to partition the edge based on a coreelement for each vertex of the core Voronoi diagram.
 24. The programproduct of claim 23, wherein the core element is one of a largestpossible core element and a smallest possible core element.
 25. Theprogram product of claim 24, wherein in the case that the core elementis the largest possible core element, the intervals are as large aspossible, and wherein in the case that the core element is the smallestpossible core element, the intervals are as small as possible.
 26. Theprogram product of claim 22, wherein the at least one dimension includesa width for each interval and a spacing to a neighboring shape for eachinterval.
 27. The program product of claim 22, wherein the at least onedimension is a function of another dimension.
 28. The program product ofclaim 22, further comprising the program code configured to use thedimensions to evaluate a check rule.
 29. The program product of claim28, wherein the check rule involves at least one of: a single edge, apair of neighboring edges, and edges within more than one layer of theIC design.
 30. An integrated circuit (IC) check rule evaluation systemcomprising: means for partitioning an edge of a shape in the IC designinto a plurality of intervals, the partitioning means including: meansfor generating a core Voronoi diagram for the shape using a firstmetric, and means for partitioning the edge based on the core Voronoidiagram; means for assigning at least one dimension to each intervalusing a second metric; and means for using the at least one dimension toevaluate a check rule.
 31. The IC check rule evaluation system of claim30, wherein the check rule is a width dependent spacing rule.